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In a class of 75 students, every student participates in at least one of the three events – music, drama and poetry. 12 students participate in all 3 events. 21 student participate in any two events. If 14 students participate in music only and 15 students participate in drama only, then how many students participate in poetry only? 

In a class of 75 students, every student participates in at least one of the three events – music, drama and poetry. 12 students participate in all 3 events. 21 student participate in any two events. If 14 students participate in music only and 15 students participate in drama only, then how many students participate in poetry only?  Correct Answer 13

Total number of students = 75.

14 students participate in music only.

15 students participate in drama only.

12 students participate in all 3 events.

21 student participate in any two events. There are three case possible:

So,

Music students + Drama students + Poetry students + All 3 participants + Any 2 participants = Total

14 + 15 + X + 12 + 21 = 75

X + 62 = 75

X = 75 – 62

X = 13.

Hence, the correct answer is 13.

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